Invertibility versus Lagrange equation for traction free energy-minimal deformations

被引：7

作者：

Iwaniec, Tadeusz ^{[1
,2
]}

Onninen, Jani ^{[1
,3
]}

机构：

[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

[2] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

[3] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla, Finland

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 52卷 / 3-4期

基金：

芬兰科学院; 美国国家科学基金会;

关键词：

MONOTONE MAPPINGS; HARMONIC-MAPPINGS; SURFACES; THEOREMS; SPACE;

D O I：

10.1007/s00526-014-0719-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X, Y subset of R-2 be bounded Jordan domains of the same topological type and h : X (onto) over right arrow Y a traction free minimal mapping for the Dirichlet energy integral. It is shown that h : O -> Y, restricted to any subdomain O subset of X, is injective if and only if it is harmonic in O. This result appears pertinent to other energy integrals and, in greater generality, may be interpreted as saying that the interpenetration of matter (under hyperelastic deformations of thin plates) is inevitable precisely in the localities where the Lagrange equation fails.

引用

页码：489 / 496

页数：8